Outlet works for two prong plugs but not for three prongs.

Might be there is a problem in the third prong on your outlet.

Probably you have "back feeding".

This is common, and it happens mostly -as an example- when some receptacles run the same circuits with lights.

You remove the receptacle from the wiring, and you have lights Off. The hot wire will be hot, the neutral will be neutral and ground will be ground.

As soon as you turn the light On, not always but it happens, the hot wire will be always hot, but the neutral wire can give you hot signal as well, and possibly the ground will do the same if somewhere in the circuit the ground and neutral are touching one to another. This happens because the loose wires you are testing are the last end and neutral and ground wires are not returning power back to grounding.

Back feeding is a huge problem when electric power is not disconnected properly.

For example, you have the main panel with two hot phases, neutral and ground wiring. You have lots of devices connected in the house receptacles.

If you disconnect the main ground wire first at the main panel, then the phases of the hot wiring will automatically travel thru the neutral wire and will cause a 220 v circuit in the 110v circuits.

Then, TVs, radios, computers, etc will be burn out because the higher voltage.

In your case, you better pull out the compromised receptacles, check if they are wired properly. You might need to pull more receptacles.

You must use a different kind of tester, with continuity.

Well, I think you might have an idea how to test that circuit following this video.

Thanks for your generous help friend. Sorry for late reply.